b: \(\Leftrightarrow2x-1+x-1+2\sqrt{\left(2x-1\right)\left(x-1\right)}=25\)
\(\Leftrightarrow2\sqrt{\left(2x-1\right)\left(x-1\right)}=25-3x+2=-3x+23\)
\(\Leftrightarrow4\left(2x-1\right)\left(x-1\right)=\left(-3x+23\right)^2\)
\(\Leftrightarrow4\left(2x^2-3x+1\right)=\left(3x-23\right)^2\)
\(\Leftrightarrow9x^2-138x+529-8x^2+12x-4=0\)
=>x^2-126x+525=0
hay \(x\in\left\{121.69;4.31\right\}\)
ĐKXĐ: \(x\ge1\)
\(\sqrt{2x-1}-3+\sqrt{x-1}-2=0\)
\(\Leftrightarrow\dfrac{2x-1-9}{\sqrt{2x-1}+3}+\dfrac{x-1-4}{\sqrt{x-1}+2}=0\)
\(\Leftrightarrow\dfrac{2\left(x-5\right)}{\sqrt{2x-1}+3}+\dfrac{x-5}{\sqrt{x-1}+2}=0\)
\(\Leftrightarrow\left(x-5\right)\left(\dfrac{2}{\sqrt{2x-1}+3}+\dfrac{1}{\sqrt{x-1}+2}\right)=0\)
\(\Leftrightarrow x=5\)
